Question

(1) On Set N, a * b = a + 2b then 2 * (3 * 4) =
​

Answer 1

Answer:

ANSWER

A+B=2B

′

..(1)

Taking transpose on both sides, we have A

′

+B

′

=2B ..(2)

3A+2B=I

3

..(3)

Taking transpose on both sides, we get 3A

′

+2B

′

=I

3

..(4)

Substituting equation (2) in (4), we have

3(2B−B

′

)+2B

′

=I

3

i.e. 6B−B

′

=I

3

Writing B

′

=

2

A+B

, we get

6B−

2

A+B

=I

3

∴12B−A−B=2I

3

i.e. 11B−A=2I

3

⇒11B−A=6A+4B

∴7B=7A

⇒A=B

Put this in equation (3)

⇒I

3

=3A+2A=5A=5B

⇒10A+5B=10A+5A=15A=3I

3